US7386431B2 - Method system and program storage device for simulating interfacial slip in a hydraulic fracturing simulator software - Google Patents
Method system and program storage device for simulating interfacial slip in a hydraulic fracturing simulator software Download PDFInfo
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Definitions
- the subject matter set forth in this specification relates to a Hydraulic Fracturing Simulator Software adapted for designing and monitoring and evaluating petroleum reservoir fracturing, and, in particular, to a Hydraulic Fracturing Simulator Software adapted for simulating a phenomenon known as ‘slip’ or ‘debonding’ between adjacent layers of an Earth formation when designing and monitoring and evaluating petroleum reservoir fracturing.
- Proppant or propping agent is carried into the fracture by a viscosified fluid, and deposited into the fracture.
- Proppant provides a permeable flow channel for formation fluids, such as oil and gas, to travel up the wellbore and to the Earth's surface.
- Fracturing involves many variables, including: viscosity of the fracturing fluid, rate of leak-off of fracturing fluid into the reservoir, proppant carrying capacity of the fluid, viscosity of the fluid as a function of temperature, time history of fluid volumes (i.e., the amount of fluid pumped over a given period of time), time history of proppant volumes, fluid physical constants, proppant properties, and the geological properties of various zones in the reservoir.
- a Hydraulic Fracturing Simulator software is capable of modeling the ‘fracturing event’.
- the Hydraulic Fracturing Simulator software will design and monitor and evaluate the ‘petroleum reservoir fracturing’ associated with the ‘fracturing event’ from a time extending before, during, and after the ‘fracturing event’.
- the Hydraulic Fracturing Simulator software designs and monitors and evaluates the ‘petroleum reservoir fracturing’ associated with the ‘fracturing event’
- the Hydraulic Fracturing Simulator software should also function to model a phenomenon known as ‘interfacial slip’ or ‘debonding’.
- Hydraulic Fracturing Simulator Software is needed that is capable of modeling or simulating the ‘interfacial slip’ or ‘debonding’ which exists between adjacent layers of an Earth formation when the Hydraulic Fracturing Simulator Software is designing and monitoring and evaluating ‘petroleum reservoir fracturing’ associated with a ‘fracturing event’.
- One aspect of the present invention involves a method of simulating a hydraulic fracture in a formation having a plurality of layers where slip exists between at least one adjacent pair of the layers, comprising: (a) calculating an influence coefficient matrix on the condition that the slip exists between at least one adjacent pair of the layers, the calculation of said matrix taking into account an existence of said slip; (b) calculating a fracture width at a first time step using the influence coefficient matrix; (c) calculating a fluid pressure at the first time step using the fracture width; and (d) updating a fracture footprint in response to the calculating step (c).
- Another aspect of the present invention involves a program storage device readable by a machine tangibly embodying a program of instructions executable by the machine to perform method steps for simulating a hydraulic fracture in a formation having a plurality of layers where slip exists between at least one adjacent pair of the layers, the method steps comprising: (a) calculating an influence coefficient matrix on the condition that the slip exists between at least one adjacent pair of the layers, the calculation of said matrix taking into account an existence of said slip; (b) calculating a fracture width at a first time step using the influence coefficient matrix; (c) calculating a fluid pressure at the first time step using the fracture width; and (d) updating a fracture footprint in response to the calculating step (c).
- Another aspect of the present invention involves a system adapted for simulating a hydraulic fracture in a formation having a plurality of layers where slip exists between at least one adjacent pair of the layers, comprising: first apparatus adapted for calculating an influence coefficient matrix on the condition that the slip exists between at least one adjacent pair of the layers, the calculation of said matrix taking into account an existence of said slip; second apparatus adapted for calculating a fracture width at a first time step using the influence coefficient matrix; third apparatus adapted for calculating a fluid pressure at the first time step using the fracture width; and fourth apparatus adapted for updating a fracture footprint in response to the calculation performed by the third apparatus.
- Another aspect of the present invention involves a program storage device readable by a machine tangibly embodying a program of instructions executable by the machine to perform method steps of simulating a hydraulic fracture in an Earth formation
- the formation includes a multilayered reservoir comprised of a plurality of layers, a slip existing between at least one adjacent pair of layers of the multilayered reservoir, the method steps comprising: setting up an influence coefficient matrix, the matrix having a plurality of numbers, the plurality of numbers of the influence coefficient matrix being calculated and determined such that the method steps for simulating the hydraulic fracture will take into account an existence of the slip between at least one adjacent pair of the layers of the multilayered reservoir.
- Another aspect of the present invention involves a method of simulating a hydraulic fracture in an Earth formation where the formation includes a multilayered reservoir comprised of a plurality of layers, a slip existing between at least one adjacent pair of layers of the multilayered reservoir, comprising the step of: setting up an influence coefficient matrix, the matrix having a plurality of numbers, the plurality of numbers of the influence coefficient matrix being calculated and determined such that the method for simulating the hydraulic fracture will take into account an existence of the slip between at least one adjacent pair of the layers of the multilayered reservoir.
- Another aspect of the present invention involves a system adapted for simulating a hydraulic fracture in an Earth formation where the formation includes a multilayered reservoir comprised of a plurality of layers, a slip existing between at least one adjacent pair of layers of the multilayered reservoir, comprising: apparatus adapted for setting up an influence coefficient matrix, the matrix having a plurality of numbers, the plurality of numbers of the influence coefficient matrix being calculated and determined such that the method for simulating the hydraulic fracture will take into account an existence of the slip between at least one adjacent pair of the layers of the multilayered reservoir.
- FIGS. 1 through 3 illustrate a typical Hydraulic Fracturing (HF) job in a wellbore
- FIG. 4 illustrates a perforated wellbore in a multilayered Earth formation that is being fractured and showing the extent of the fracture, or fracture footprint, at times t 1 , t 2 , t 3 , . . . , t n ;
- FIG. 5 illustrates the fracture shown at time t n in FIG. 4 which has been taken along section line 5 - 5 of FIG. 4 ;
- FIGS. 6 and 7 illustrate a fracture footprint created in the formation penetrated by the wellbore when the HF job is pumped
- FIG. 8 illustrates how a numerical mesh comprised of a plurality of active and inactive grid cells or elements will overlay on top of the fracture footprint of FIG. 7 , each grid cell of the mesh having a width and pressure, some of the grids cells called ‘tip elements’ being intersected by a perimeter of the fracture footprint, the tip elements having a width and a pressure (w, p), a portion of each tip element having fracturing fluid disposed therein;
- FIG. 9 illustrates an apparatus used in connection with a Hydraulic Fracturing (HF) job adapted for fracturing a formation penetrated by a wellbore, the apparatus including a computer system for storing a software therein called a ‘Hydraulic Fracturing Simulator software’;
- HF Hydraulic Fracturing
- FIG. 10 illustrates the computer system of FIG. 9 which stores the software called a ‘Hydraulic Fracturing Simulator software’ adapted for modeling ‘interfacial slip’ or ‘debonding’ between adjacent Earth formation layers during a ‘petroleum reservoir fracturing’ event;
- a ‘Hydraulic Fracturing Simulator software’ adapted for modeling ‘interfacial slip’ or ‘debonding’ between adjacent Earth formation layers during a ‘petroleum reservoir fracturing’ event;
- FIG. 11 illustrates in greater detail the ‘Other Data’ of FIG. 10 ;
- FIG. 12 illustrates the ‘Other Software Instructions’ of FIG. 10 ;
- FIG. 13 illustrates a construction of the ‘Hydraulic Fracturing Simulator software’ of FIG. 10 ;
- FIG. 14 illustrates the function practiced by the ‘Set Up Influence Coefficient Matrix [C]‘step in the ‘Hydraulic Fracturing Simulator software’ of FIG. 13 ;
- FIGS. 15 and 16 illustrate a more detailed construction of the ‘Hydraulic Fracturing Simulator software’ which is illustrated in FIG. 13 ;
- FIGS. 17 and 18 illustrate a flowchart which illustrates a construction of the computation of the ‘Influence Coefficient Matrix’ in the ‘Set Up Influence Coefficient Matrix’ step of FIG. 13 and the ‘Generate Elastic Influence Coefficient Matrix for Parent Mesh’ step of FIG. 15 ;
- FIG. 19 is a numerical mesh which is used in conjunction with the flowcharts illustrated in FIGS. 17 and 18 .
- This specification discloses a Hydraulic Fracturing Simulator software adapted to be stored in a memory of a program storage device of a computer system for modeling and simulating an ‘interfacial slip’ or ‘debonding’ between adjacent layers of an Earth formation when the Hydraulic Fracturing Simulator software is designing and monitoring and evaluating petroleum reservoir fracturing.
- the Hydraulic Fracturing Simulator software includes a first step further including the step of ‘Setting Up an Influence Coefficient Matrix’ and a second step further including two iteration loops whereby, in a first iteration loop at a first time step, a second iteration loop will continuously calculate fracture width for each element of the mesh given a previously determined fluid pressure and will continuously calculate fluid pressure for each element of the mesh given a previously determined fracture width at which time the fracture footprint is updated to a first value, then, in the first iteration loop at a second time step, the second iteration loop continuously calculates fracture width for each element of the mesh given a previously determined fluid pressure and continuously calculates fluid pressure for each element of the mesh given a previously determined fracture width at which time the fracture footprint is updated to a second value, and the process repeats until the solution converges to a prescribed tolerance, at which point, Output Data is generated.
- the Output Data includes the previously determined first value of the fracture footprint, the previously determined second value of the fracture footprint, . . . , and the previously determined ‘nth’ value of the fracture footprint for additional time steps.
- the Output data representative of the updated fracture footprint at each of the incremented time steps, is generated and is recorded or displayed on a recorder or display device.
- the Influence Coefficient Matrix is calculated and determined in a special way such that, when the Influence Coefficient Matrix is determined, and during any ‘fracturing event’, the Hydraulic Fracturing Simulator software will model and simulate the ‘interfacial slip’ or ‘debonding’ which takes place between adjacent layers of an Earth formation, as indicated in FIGS. 4 and 5 .
- Linear springs can be used to represent slip on layer interfaces in layered formations in an approximate manner.
- a rigorous approach would invoke a frictional law, such as Mohr-Coulomb, to model slip on interfaces.
- the aforementioned concept of linear springs (hereinafter, the ‘linear spring concept’) allows one to rigorously reduce computational effort at the expense of compromising on physical behavior.
- the ‘linear spring concept’ can be embedded in a variety of different algorithms that perform multi-layer elasticity calculations.
- the ‘linear spring concept’ can be used in connection with multi-layer elasticity formulations adapted for use in Planar 3D hydraulic fracturing simulators.
- a corresponding method, involving the ‘linear spring concept’ in connection with multi-layer elasticity formulations in Planar 3D hydraulic fracturing simulators, would model interfacial slip (or debonding) in layered reservoirs adapted for use in hydraulic fracturing simulators.
- the ‘linear spring concept’ can be used to model interfacial slip (or debonding) when based on a mathematical framework involving a boundary element method scheme in a multi-layered elasticity solution.
- a method and system and program storage device which is adapted for modeling interfacial slip in layered reservoirs by calculating an Influence Coefficient Matrix [C] in a ‘special way’, the calculation of the ‘Influence Coefficient Matrix [C]’ in the ‘special way’ using a ‘linear springs’ concept adapted for use in hydraulic fracturing simulators.
- the ‘linear springs’ concept is used to model interfacial slip based on a mathematical framework involving a boundary element method scheme in a multi-layered elasticity solution.
- a perforating gun 10 is disposed in a wellbore 12 and a packer 14 isolates a plurality of shaped charges 16 of the perforating gun 10 downhole in relation to the environment uphole.
- the shaped charges 16 detonate and a corresponding plurality of perforations 18 are produced in a formation 17 penetrated by the wellbore 12 .
- a fracturing fluid 22 is pumped downhole into the perforations 18 in accordance with a particular pumping schedule 24 .
- the formation 17 surrounding the perforations 18 is fractured.
- oil or other hydrocarbon deposits 26 begin to flow from the fractures, into the perforations 18 , into the wellbore 12 , and uphole to the surface.
- the oil or other hydrocarbon deposits flow at a certain ‘production rate’ 28 (e.g., in m 3 /day).
- FIG. 4 a perforated wellbore 12 in a multilayered, hydraulically fractured Earth formation 17 is illustrated.
- a tubing is disposed in the wellbore 12 , and the formation 17 penetrated by the wellbore 12 is perforated by detonating a plurality of shaped charges 16 which are disposed in the tubing, as shown schematically in FIG. 4 .
- FIG. 4 schematic snapshots of one hydraulic fracture 32 shown at a series of time steps are depicted at times t 1 , t 2 , t 3 , . . . , t n as denoted by the ‘Planar 3D hydraulic fracture model’ 25 shown in FIG. 4 .
- the formation 17 includes a plurality of layers 17 a , 17 b , 17 c , 17 d , 17 e , 17 f , 17 g , 17 h , 17 i , and 17 j .
- Each of the layers 17 a - 17 j can be characterized by a Young's Modulus (E) and a Poisson's Ratio ( v).
- the Young's Modulus (E) and the Poisson's Ratio (v) describe the elastic properties of each of the layers 17 a - 17 j in FIG. 4 .
- the elastic properties of layer 17 a can be characterized by Young's Modulus and Poisson's Ratio (E a , v a ), the elastic properties of layer 17 b being characterized by Young's Modulus and Poisson's Ratio (E b , v b ), the elastic properties of layer 17 c being characterized by Young's Modulus and Poisson's Ratio (E c , v c ), the elastic properties of layer 17 d being characterized by Young's Modulus and Poisson's Ratio (E d , V d ), the elastic properties of layer 17 e being characterized by Young's Modulus and Poisson's Ratio (E e , v e ), the elastic properties of layer 17 f being characterized by Young's Modulus and Poisson's Ratio (E f , v f ), the elastic properties of layer 17 g being characterized by Young's Modulus and Poisson's Ratio
- a 'slip’ region 27 also known as a ‘debonding’ region 27 .
- the adjacent layers of the formation 17 such as adjacent layer 17 f relative to layer 17 e and adjacent layer 17 h relative to 17 g , may 'slip’ or ‘debond’ relative to one another.
- FIG. 4 represents the degree to which the adjacent layers of the formation 17 (such as layers 17 e and 17 f ) will slip relative to one another when the fracture at times t 1 , t 2 , t 3 , . . . , t n is pressurized by the fracturing fluid.
- the hydraulic fracture shown at times t 1 , t 2 , t 3 , . . . , t n in FIG. 4 is created, stresses and strains are produced in the surrounding reservoir rock.
- a slip 27 may be induced at the interface between adjacent layers of the formation 17 , such as between layers 17 e and 17 f of the formation 17 , or between layers 17 g and 17 h of the formation 17 , or between any other adjacent layers, as shown in FIG. 4 .
- the two sections of rock may slide or ‘slip’ relative to one another, and/or even ‘debond’ relative to each other.
- the ‘Hydraulic Fracturing Simulator Software’ 80 will allow the interfaces between the different layers 17 a - 17 j to slip (see slip 27 ) relative to one another when the fracture 32 at times t 1 , t 2 , t 3 , . . . , t n is pressurized by the fracturing fluid.
- the ‘Hydraulic Fracturing Simulator Software’ 80 of FIG. 10 will calculate the degree of slip 27 which takes place between the adjacent layers 17 a - 17 j of the formation 17 , such as between adjacent layers 17 e and 17 f or between adjacent layers 17 g and 17 h.
- FIG. 5 a cross section schematic of the Earth formation 17 of FIG. 4 taken along section line 5 - 5 of FIG. 4 is illustrated.
- the wellbore 12 penetrates the Earth formation 17 and a hydraulic fracture 29 is shown between layers 17 e and 17 h .
- the fracture 29 has a certain ‘fracture width’ 29 a which was created in response to the pressurization of the formation 17 by the fracturing fluid.
- the fracture 29 has a fracture width 29 a because the ‘rock mass’ surrounding layer 17 g has been ‘deformed’. In fact, since the fracture 29 produces a ‘deformation’ in the ‘rock mass’ thereby creating the fracture width 29 a as shown in FIG.
- any point within the formation 17 will feel a certain stress and strain and therefore any point within the formation 17 will exhibit some ‘deformation’ of the ‘rock mass’.
- the ‘deformations’ of the ‘rock mass’ will be different at each point within the formation 17 of FIG. 5 .
- some slip 27 may occur at the interfaces between adjacent layers of the formation 17 , such as at the interfaces between layers 17 e and 17 f in FIG. 5 .
- some debonding may also occur at the interfaces between adjacent layers, such as at the interfaces between adjacent layers 17 e and 17 f of FIG. 5 .
- the reservoir rock at the interface faces of interface 31 can debond, or slip, relative to one another, as indicated at slip 27 in FIG. 5 .
- fluid can propagate within the slip 27 at the interface 31 .
- the slip 27 in FIG. 5 can: (1) stop the growth of the fracture 29 , and (2) control the height of the fracture 29 . Therefore, it is important to model the slip 27 of FIG. 5 and its effect on the fracture 29 of FIG. 5 .
- the ‘Hydraulic Fracturing Simulator Software’ 80 of FIG. 10 will model the slip 27 and its effect on the fracture 29 in FIG. 5 .
- FIGS. 6 and 7 a simplified schematic three dimensional view of the fracture footprint 32 of FIG. 4 , is illustrated.
- the fracture footprint 32 has a length ‘L’ and a height ‘H’ and a width ‘w’.
- FIG. 7 the wellbore 12 is illustrated again, and a plurality of perforations 18 are created in the formation 17 penetrated by the wellbore 12 , as illustrated in FIGS. 1-3 .
- the formation 17 includes a plurality of different layers 17 a - 17 j .
- FIG. 6 a simplified schematic three dimensional view of the fracture footprint 32 of FIG. 4 .
- the fracture footprint 32 has a length ‘L’ and a height ‘H’ and a width ‘w’.
- FIG. 7 the wellbore 12 is illustrated again, and a plurality of perforations 18 are created in the formation 17 penetrated by the wellbore 12 , as illustrated in FIGS. 1-3 .
- the formation 17 includes a plurality of different layers 17 a - 17 j .
- the ‘fracture footprint’ 32 is created in the formation 17 which is similar to the fracture footprint 32 shown in FIG. 4 that is created over the different periods of time t 1 , t 2 , t 3 , . . . , t n .
- the ‘fracture footprint’ 32 in FIG. 7 has a cross section 44 , the cross section 44 having a fracture width ‘w’ similar to the width ‘w’ of the fracture footprint 32 shown in FIG. 6 .
- a numerical mesh 48 comprised of a plurality of grid-elements 48 a or grid cells 48 a overlays over the top of the fracture footprint 32 .
- the fracture footprint 32 is assumed (by the model of this specification) to lie in the 2D plane, although, in principle and in reality, the fracture footprint 32 does lie in the 3D plane.
- the mesh 48 includes a plurality of active elements or active grid cells 48 a 1 and a plurality of inactive elements or inactive grid cells 48 a 2 .
- the active grid cells 48 a 1 will overlay the fracture footprint 32
- the inactive grid cells 48 a 2 will not overlay the fracture footprint 32 .
- each of the active grid elements or grid cells 48 a 1 of the mesh 48 has a width ‘w’ and a pressure ‘p’ assigned thereto, denoted by the symbol: (w, p). Therefore, each active grid cell 48 a 1 of the mesh 48 has a width/pressure value (w, p) assigned to that active grid cell.
- FIG. 7 since the fracturing fluid propagating down the wellbore 12 enters the perforations 18 and creates the fracture footprint 32 , in FIG. 8 , each of the active grid cells 48 a 1 in the mesh 48 has a fracturing fluid disposed therein.
- FIG. 8 since the fracturing fluid propagating down the wellbore 12 enters the perforations 18 and creates the fracture footprint 32 , in FIG. 8 , each of the active grid cells 48 a 1 in the mesh 48 has a fracturing fluid disposed therein.
- active grid cells 48 a 1 there are two types of active grid cells 48 a 1 : (1) an active grid cell 48 a 1 which is intersected by a perimeter 46 a of the fracture footprint 32 , and (2) an active grid cell 48 a 1 which is not intersected by the perimeter 46 a of the fracture footprint 32 .
- An active grid cell 48 a 1 that is intersected by the perimeter 46 a of the fracture footprint 32 is known as a ‘tip element’.
- ‘tip element’ 50 is an active grid cell 48 a 1 that is intersected by the perimeter 46 a of the fracture footprint 32 .
- An active grid cell 48 a 1 which is not intersected by the perimeter 46 a of the fracture footprint 32 has a volume which is wholly occupied by the fracturing fluid (i.e., 100% of the active grid cell is occupied by the fracturing fluid), where the fracturing ‘fluid’ may or may not include proppant.
- active grid cell 52 is not intersected by the perimeter 46 a of the fracture footprint 32 and its volume is wholly occupied by the fracturing fluid (100% of the volume of the active grid cell 52 is occupied by fracturing fluid).
- an active grid cell 48 a 1 that is intersected by the perimeter 46 a is occupied by ‘less than 100%’ of the fracturing fluid.
- the active grid cell or ‘tip element’ 54 is intersected by the perimeter 46 a of the fracture footprint 32 , however, only 45% of the pore volume of the active grid cell 54 is occupied by the fracturing fluid.
- an inactive grid cell 48 a 2 such as inactive grid cell 55 , has a volume which is wholly devoid of any fracturing fluid (0% of the volume of the inactive grid cell 55 is occupied by fracturing fluid).
- the ‘VOF software’ of that prior pending application calculates, over a series of time steps, the ‘amount of fracturing fluid that is contained within each of the active grid cells 48 a 1 that are intersected by the perimeter 46 a of the fracture footprint 32 ’.
- the ‘VOF software’ of prior pending application Ser. No. 10/831,799 calculates, over the series of time steps, the ‘amount of fracturing fluid that is contained within each of the tip elements 50 ’.
- the ‘amount of fracturing fluid that is contained within each of the tip elements 50 ’ is calculated from the ‘fill fraction’, the ‘fill fraction’ being denoted by the letter ‘F’.
- the ‘fill fraction’ F for the ‘tip element’ 54 is 45%. Therefore, the ‘VOF software’ of prior pending application Ser. No. 10/831,799 calculates, over a series of time steps, the ‘fill fraction’ (F) for each of the ‘active grid cells 48 a 1 of the mesh 48 that is intersected by the perimeter 46 a of the fracture footprint 32 ’. That is, the ‘VOF software’ of prior pending application Ser. No.
- 10/831,799 calculates, over the series of time steps, the ‘fill fraction’ (F) for each of the ‘tip elements’ 50 of the mesh 48 of FIG. 8 .
- the amount or degree by which the perimeter 46 a of the footprint 32 of the fracture is expanding (or contracting), as a result of the pumping of the fracturing fluid into the perforations 18 in the formation 17 by the pump trucks can be determined.
- the pump trucks 23 of FIG. 4 will pump a fracturing fluid 62 (frac fluid and proppant 62 ) down the wellbore 12 in accordance with a pumping schedule 60 (an example used in connection with this discussion).
- the fracturing fluid 62 will enter the perforations 18 , and, responsive thereto, create a ‘fracture footprint’ 32 , similar to the fracture footprint 32 shown in FIG. 7 .
- Micro-seismic data sensor(s) 64 and tiltmeter data or other sensor(s) 66 will monitor the approximate geometry of the fracture footprint 32 and, responsive thereto, the sensor(s) 64 and 66 will generate output signals, the micro-seismic data sensor(s) 64 generating a micro-seismic data output signal 64 a , the tiltmeter data sensor(s) 66 generating a tiltmeter data output signal 66 a , and the pumping schedule 60 generating a pumping schedule output signal 60 a representative of the pumping schedule 60 .
- the pumping schedule output signal 60 a , the tiltmeter data output signal 66 a , and the micro-seismic data output signal 64 a are time line merged via a ‘time line merging’ step 68 .
- the pumping schedule output signal 60 a , the tiltmeter data output signal 66 a , and the micro-seismic data output signal 64 a are ‘time synchronized’ in a particular manner such that the tiltmeter data output signal(s) 66 a and the micro-seismic data output signal(s) 64 a are synchronized with the times present in the pumping schedule 60 .
- a ‘time line merged pumping schedule and tiltmeter data and micro-seismic data’ output signal 70 is generated which is provided as ‘input data’ (see ‘input data’ 82 of FIG. 10 ) to a ‘computer system’ 72 optionally disposed within a truck 74 situated at the site of the wellbore, such as a monitoring truck 74 or a ‘FracCAT vehicle’ 74 (which is a vehicle with software that monitors and measures the fracture and controls the fracture treatment).
- the ‘computer system’ 72 which is disposed within the truck 74 of FIG. 9 , such as the ‘FracCAT vehicle’ 74 , is illustrated.
- the ‘time line merged pumping schedule and tiltmeter data and micro-seismic data’ output signal 70 of FIG. 9 is provided as the ‘input data’ 82 to the computer system 72 disposed within the truck 74 , the output signal 70 being comprised of a time line merged pumping schedule and tiltmeter data and micro-seismic data plus other data including downhole temperature and bottom hole pressure.
- the 10 includes a processor 72 a operatively connected to a system bus, a memory or other program storage device 72 b operatively connected to the system bus, and a recorder or display device 72 c operatively connected to the system bus.
- the memory or other program storage device 72 b stores the following software ( 76 , 78 , and 80 ): a Planar 3D User Interface software 76 , a Planar 3D ‘engine’ or software 78 , and a Hydraulic Fracturing Simulator Software 80 .
- the software 76 , 78 , and 80 which is stored in the memory 72 b of FIG. 10 , can be initially stored on a CD-ROM, where that CD-ROM is also a ‘program storage device’.
- That CD-ROM can be inserted into the computer system 72 , and, then, the software 76 , 78 , and 80 , which includes the Hydraulic Fracturing Simulator Software 80 , can be loaded from that CD-ROM and into the memory/program storage device 72 b of the computer system 72 of FIG. 10 .
- the Hydraulic Fracture Simulator Software 80 will be described in detail in the following paragraphs because the software 80 will model the ‘interfacial slip’ or ‘debonding’ which occurs between adjacent layers of the Earth formation.
- the computer system 72 of FIG. 10 receives Input Data 82 , which includes: (1) time line merged pumping schedule, tiltmeter data, and micro-seismic data 84 , and (2) Other Data 86 .
- the computer system 72 also receives Other Software Instructions 88 .
- the processor 72 a will execute the Hydraulic Fracturing Simulator Software 80 (including the Planar 3D User Interface software 76 and the Planar 3D ‘engine’ 78 ), while simultaneously using the Input Data 82 and Other Software Instructions 88 ; and, responsive thereto, the recorder or display device 72 c will generate a set of ‘Output Data’ 72 c 1 which is adapted to be recorded by or displayed on the recorder or display device 72 c .
- the computer system 72 may be a personal computer (PC), a workstation, or a mainframe.
- the memory or program storage device 72 b is a computer readable medium or a program storage device which is readable by a machine, such as the processor 72 a .
- the processor 72 a may be, for example, a microprocessor, microcontroller, or a mainframe or workstation processor.
- the memory or program storage device 72 b which stores the Hydraulic Fracturing Simulator Software 80 , may be, for example, a hard disk, ROM, CD-ROM, DRAM, or other RAM, flash memory, magnetic storage, optical storage, registers, or other volatile and/or non-volatile memory.
- the Other Data 86 and the Other Software Instructions 88 of FIG. 10 is illustrated.
- the Other Data 86 will include: layer confining stresses and properties, perforating interval and depth, wellbore data, fluid and proppant properties, time history of fluid volumes to be pumped, time history of proppant volumes to be pumped, and logs identifying the identity, properties, and location of geological zones.
- the Other Software Instructions 88 include instructions to calculate values representing physical dimensions of the fracture and pressures inside the fracture.
- the Hydraulic Fracturing Simulator Software 80 includes: an initial ‘time stepping’ step 90 , a second step 92 which calculates fracture width (w) given the fluid pressure (p); a third step 94 which calculates fluid pressure (p) given the fracture width (w); and a fourth step 96 adapted to update the fracture footprint.
- the fracture ‘footprint’ 32 is shown in FIGS. 4 and 13 at times t 1 , t 2 , t 3 , . . . , t n .
- time stepping loop 98 in FIG. 13 wherein the ‘time stepping’ step 90 will increment from a first time step (t 1 ), to a second time step (t 2 ), to a third time step (t 3 ), . . . , and to an nth time step (t n ).
- the second step 92 and the third step 94 will iterate on each other (as indicated by arrow 100 ) until the fracture width (w) and the fluid pressure (p) are solved at every point in the fracture geometry of FIG. 4 .
- the fracture footprint is updated in step 96 .
- the proppant concentration is calculated for each grid cell in the updated fracture footprint.
- the ‘output data’ 72 c 1 associated with the last iteration loop 100 , is generated and stored. ‘Convergence’ takes place when the ‘solution does not change from one iteration to the next’.
- the time step 90 is then incremented to the second time step t 2 , and, responsive thereto, the second step 92 and the third step 94 will then iterate again on each other (as indicated by arrow 100 ) until the fracture width (w) and the fluid pressure (p) are solved at every point in the fracture geometry of FIG. 4 .
- the fracture footprint is updated in step 96 .
- the proppant concentration is calculated for each grid cell in the updated fracture footprint.
- the ‘output data’ 72 c 1 associated with the last iteration loop 100 , is generated and stored.
- the time step 90 is then incremented once again to the third time step t 3 , the second step 92 and the third step 94 will then iterate again on each other (as indicated by arrow 100 ) until the fracture width (w) and the fluid pressure (p) are solved at every point in the fracture geometry of FIG. 4 .
- the fracture footprint is updated in step 96 .
- the proppant concentration is calculated for each grid cell in the updated fracture footprint.
- the ‘output data’ 72 c 1 associated with the last iteration loop 100 , is generated and stored.
- the time step 90 is then incremented once again, and the above process repeats until a user specified time is reached.
- the inner iteration loop 100 is solving for two values: (1) fracture width (w) using the ‘elasticity equation’, and (2) fluid pressure (p) using the ‘fluid flow equations’.
- fracture width (w) using the ‘elasticity equation’
- p fluid pressure
- the aforesaid ‘convergence’ will be achieved when the difference between the fracture width (w) of step 92 in the current iteration of loop 100 and the fracture width (w) of step 92 in the previous iteration of loop 100 is less than or equal to a small value ⁇ , and the difference between the fluid pressure (p) of step 94 in the current iteration of loop 100 and the fluid pressure (p) of step 94 in the previous iteration of loop 100 is less than or equal to a small value ⁇ .
- the Output Data 72 c 1 is generated at the end of each time step.
- ‘additional output data’ 99 is generated when the time stepping in the outer iteration loop 98 is complete, the ‘additional output data’ 99 being used in subsequent calculations, such as in the generation of other graphical plots.
- steps 92 and 94 can be solved in various ways, such as by iteration of two equations as shown here, or by direct substitution of the results of one equation into the other equation, or vice-versa.
- a first step 102 is practiced, the first step 102 being called ‘Set Up Influence Coefficient Matrix [C]’ 102 .
- the ‘Set Up Influence Coefficient Matrix [C]’ step 102 of FIG. 13 will be discussed below with reference to FIG. 14 of the drawings.
- step 92 will calculate the fracture width (w) using the ‘Elasticity Equation’ and step 94 will calculate the fluid pressure (p) using the ‘Fluid Flow Equations’.
- the fracture width (w) of step 92 is actually calculated by using an ‘Elasticity Equation’ 33 .
- FIG. 14 a generic form of the ‘Influence Coefficient Matrix [C]’ 37 is shown, where the ‘Influence Coefficient Matrix [C]’ 37 has ‘M’ rows and ‘M’ columns.
- the ‘Influence Coefficient Matrix [C]’ 37 is fully populated with numbers 43 and is used to calculate fracture width (w) for step 92 in FIG. 13 .
- the ‘elasticity equation’ 33 usually assumes that all layers in a reservoir are fully bonded and, as a result, there exists no ‘slip’ 27 or other debonding between adjacent layers of a reservoir, such as between layers 17 e and 17 f of FIG. 4 . However, in a real reservoir, ‘slip’ 27 could exist between adjacent layers of a reservoir.
- the Hydraulic Fracturing Simulator software 80 disclosed in this specification will model the effect of, or take into account the existence of, the ‘slip’ 27 which may exist between adjacent layers of a reservoir (such as between layers 17 e and 17 f of FIG. 4 ). Consequently, in order for the Hydraulic Fracturing Simulator software 80 to model the effect of, or take into account the existence of, the ‘slip’ 27 which may exist between adjacent layers of a reservoir, it is necessary to calculate the ‘Influence Coefficient Matrix [C]’ 37 in the ‘Elasticity Equation’ 33 in a special way (which follows FIGS.
- FIGS. 15 and 16 a more detailed construction of the Hydraulic Fracturing Simulator Software 80 of FIG. 13 , which is disposed within the Planar 3D software 78 and the Planar 3D User Interface 76 , is illustrated.
- the Input Data 82 is provided from the human interface, such as the pumping schedule, which includes the injection rate and the proppant as a function of time, proppant concentration, fluid viscosity, the geology or the properties of the elastic layers of the reservoir including the elastic constants comprising the Young's Modulus and the Poisson's Ratio (E, v) as previously described, and the leakoff behavior.
- the human interface such as the pumping schedule, which includes the injection rate and the proppant as a function of time, proppant concentration, fluid viscosity, the geology or the properties of the elastic layers of the reservoir including the elastic constants comprising the Young's Modulus and the Poisson's Ratio (E, v) as previously described, and the leakoff behavior.
- the ‘Generate Layer Interface Locations’ step 116 the depths of each of the ‘interfaces’ ( 31 of FIG. 5 ) of the ‘layers’ ( 17 a - 17 j of FIG. 5 ) of FIG.
- step 118 the spring constants for each layer interface are assigned to each of the ‘layers’ (of FIG. 4 ) the depths of which were calculated in step 116 .
- a parent mesh is assigned to the ‘fracture’, where the parent mesh is divided into rectangular ‘elements’. See FIG. 8 for an example of the parent mesh with rectangular ‘elements’.
- the parent mesh is broken down into intersecting rows and columns comprising ‘grids’ or ‘elements’ which are generally rectangular in shape. It is assumed that the ‘fracture’ will grow into the ‘elements’ of the parent mesh, but no further.
- the numerical parent mesh is generated; that is, in step 122 , the ‘coordinates’ of each ‘grid cell’ or ‘element’ of the parent mesh are generated.
- the ‘coordinates’ will define where each ‘grid cell’ or ‘element’ exists within an axis system, such as the (x, y) axis system (and recall that the fracture footprint 46 of FIG. 8 is assumed, by the model of this specification, to lie in the 2D plane, although, in principle and in reality, the fracture footprint 46 does lie in the 3D plane). Therefore, in step 122 of FIG. 15 , the ‘coordinates’ of each of the ‘grid cells’ (such as ‘grid cells’ 48 shown in FIG.
- the next step is the ‘Generate Elastic Influence Coefficient Matrix for Parent Mesh’ step 102 , which is the same step as the ‘Set up Influence Coefficient Matrix [C]’ step 102 of FIG. 13 .
- the Influence Coefficient Matrix [C] ( 37 of FIG. 14 ) is generated. As previously mentioned, the Influence Coefficient Matrix [C] ( 37 as shown in FIG.
- each of the ‘numbers’ 43 of the Influence Coefficient Matrix [C] will indicate how one ‘element’ of the mesh relates to another ‘element’ of the mesh in an ‘elastic manner’. For example, if a fracture exists within one ‘element’ of the mesh, the numbers 43 indicate what kind of stress or strain exists within another ‘element’ of the mesh in response thereto (a phenomenon that is called an ‘elasticity behavior’).
- Each of the ‘numbers’ 43 in the Influence Coefficient Matrix [C] 37 describe this ‘elasticity behavior’.
- the Influence Coefficient Matrix [C] ( 37 of FIG. 14 ) is a matrix that indicates how one ‘element’ of the parent mesh (such as the mesh shown in FIG. 8 ) talks to another ‘element’ of the parent mesh in an ‘elastic manner’. This phenomenon will be discussed later in the functional description. Therefore, step 102 of FIGS. 13 and 15 (i.e., the ‘Set Up Influence Coefficient Matrix’ step 102 of FIG. 13 and the ‘Generate Elastic Influence Coefficient Matrix for Parent Mesh’ step 102 of FIG. 15 ), which determines the Influence Coefficient Matrix 37 of FIG. 14 , is responsible for allowing the Hydraulic Fracturing Simulator Software 80 of FIGS. 10 and 13 to simulate the ‘slip’ 27 or the ‘debonding’ 27 of FIGS. 4 and 5 .
- the loop 98 which represents a time stepping loop. The loop 98 controls how the fracture grows as a function of time during the duration of the pumping schedule.
- step 126 at any particular time step, the fracture will have propagated to some extent in the parent mesh, which is called the ‘footprint’ of the fracture; step 126 will sweep through all the ‘grid cells’ or ‘elements’ in the entire parent mesh, and then step 126 will determine if a particular ‘element’ or ‘grid cell’, within the perimeter of the ‘fracture footprint’, is an ‘inactive element’, or an ‘active element’, or a ‘partially active element’.
- step 128 entitled ‘Extract Elastic Influence Coefficient Matrix for Current Fracture Geometry’ the Influence Coefficient Matrix [C] 37 , as previously described with reference to step 102 , contains ‘all possible combinations within the parent mesh’; and, at any particular time step, we need a subset of the aforementioned ‘all possible combinations within the parent mesh’; thus, step 128 extracts, from the Influence Coefficient Matrix [C] 37 , a ‘submatrix’ which contains essential information regarding the current size of the ‘fracture footprint’.
- step 130 entitled ‘Assign Special Characteristics to Coefficients for Tip Elements’ a ‘particular subset’ of the ‘grid cells’ or ‘elements’ of the parent mesh will cross a ‘perimeter of the fracture footprint’; in connection with only the ‘particular subset’ of the ‘grid cells’ which cross the ‘perimeter of the fracture footprint’, it is necessary to change some of the properties of the ‘submatrix’ (and recall that the ‘submatrix’ contains essential information regarding the current size of the ‘fracture footprint’); step 130 will make this change to the ‘submatrix’.
- step 132 entitled ‘Assign Loading (Fluid Pressure) to Each Element in Current Mesh’ we now have a current time step and a current fracture footprint; in addition, each ‘active element’ has a ‘fluid pressure’; thus, step 132 will assign a ‘fluid pressure’ to each ‘element’ of the parent mesh.
- step 92 entitled ‘Solve Elastic Equation System for Fracture Widths’ we use the ‘Elasticity Equation’ 33 of FIG. 14 (including their Fourier Transforms) to solve for the ‘fracture width’ in each ‘element’ or ‘grid cell’ of the parent mesh (of FIG.
- step 8 at the current time step, given the ‘fluid pressure’ that was assigned to each ‘element’ of the mesh in step 132 .
- step 134 entitled ‘Calculate Influence Matrix for Fluid Flow in Current Mesh Using Widths from Above’
- step 94 entitled ‘Solve Fluid Flow Equations for Fluid Pressure in Current Mesh’
- step 94 whereby, when the ‘fluid pressures’ are determined in step 94 , those ‘fluid pressures’ determined from step 94 are used to solve for ‘fracture widths’ in step 92 , and that loop 100 will continue to process as indicated until ‘global mass balance’ is achieved in step 136 .
- step 136 to step 132 an inner iteration will take place; in that inner iteration, we continue to iterate on fluid pressure and fracture width until convergence of the solution takes place at that time step; convergence takes place when the solution does not change from one iteration to the next.
- the inner iteration loop 100 is solving for two values: (1) fracture width using the ‘Elasticity Equation’ 33 , and (2) the fluid pressure using the ‘fluid flow equations’; when the change in each of these ‘equations’ is below a tolerance, we know that the inner iteration 100 has converged.
- Steps 138 , 96 , and 140 involve updating for the next time step.
- Step 138 (‘Calculate Local Fracture Tip Velocity of Propagation’)
- step 96 (‘Grow Fracture: Update New Layout’) are described in prior pending application Ser. No. 10/831,799, filed Apr.
- step 97 the proppant concentration is calculated for each grid cell in the updated fracture footprint.
- the ‘output data’ 72 c 1 associated with the last iteration of loop 100 , is generated and stored.
- step 140 if the ‘time’ is greater than the maximum allowed, ‘additional output data’ 99 is generated, the ‘additional output data’ 99 being stored in a storage device, such as the memory or program storage device 72 b of FIG. 16 .
- the ‘additional output data’ 99 is used in subsequent calculations, such as in the generation of other graphical plots.
- the Output Data 72 c 1 includes, at each time step, the fluid pressure (p) and the fracture width (w) at each of the ‘elements’ or ‘grid cells’ 48 a 1 of FIG. 8 or ‘elements’ 67 a and 67 b of FIG. 19 (again, at each time step). Since the Output Data 72 c 1 includes fluid pressure (p) and fracture width (w) for each ‘grid cell’ or ‘element’ of FIGS. 8 and 19 at each time step, the Output Data 72 c 1 can also include a number of 2D or 3D plots representative of the fluid pressure (p) and the fracture width (w) at each of the ‘elements’ or ‘grid cells’ of FIGS.
- Steps 92 , 134 , and 94 can be solved in various ways, such as by iteration of the two equations shown here (i.e., the ‘elasticity equation’ and the ‘fluid flow equation’), or by direct substitution of the results of one equation into the other equation, or vice-versa.
- FIGS. 17 and 18 a detailed construction of the ‘Set Up Influence Coefficient Matrix’ step 102 of FIG. 13 and the ‘Generate Elastic Influence Coefficient Matrix for Parent Mesh’ step 102 of FIG. 15 is illustrated (note that step 102 of FIG. 13 is the same step as step 102 in FIG. 15 ).
- FIGS. 17 and 18 a flowchart is illustrated which depicts how the numbers 43 in the ‘Influence Coefficient Matrix [C]’ 37 are changed in order to allow the ‘Hydraulic Fracturing Simulator software’ 80 of FIG. 10 to model and ‘take into account the existence of’ the ‘slip’ 27 and/or the ‘debonding’ 27 which may exist between adjacent layers of a reservoir.
- FIGS. 17 and 18 depicts the series of steps needed to recalculate the ‘Influence Coefficient Matrix [C]’ 37 for the case when any ‘layer interfaces’ may ‘slip’ 27 or ‘debond’ 27 , such as the interfaces between layers 17 e / 17 f , and between layers 17 g / 17 h of FIG. 4 .
- step 47 initial ‘input data’ is supplied to the algorithm, such as the layer elastic Young's modulus E l and Poisson's ratio v l , layer thickness d l , and linear spring constants k yx l and k yz l , where l is the layer interface number.
- the linear spring constants k yx l and k yz l are used to ascribe physical stiffnesses to each layer interface, and relate directly the ‘interfacial shear stresses’ to the ‘shear displacements’.
- the term ‘x(1:nelemx)’ of the input data 47 refers to the x direction, with a maximum of ‘nelemx’ elements in the x direction 63 of FIG. 19 ; and, with respect to the term ‘y(1:nelemy)’ of the input data 47 , the term ‘y(1:nelemy)’ refers to the y direction, with a maximum of ‘nelemy’ elements in the y direction 61 of FIG. 19 .
- the term ‘1:nelemx’ represents a loop from “1, 2, 3, . . .
- each rectangularly shaped element or ‘grid cell’ 67 a , 67 b of FIG. 19 has a local dimension of ‘2a by 2b’ in the x and y directions 63 and 61 of FIG. 19 , respectively.
- step 49 we loop through each “sending” element iys of the numerical mesh 67 of FIG. 19 in a direction that is orthogonal to the direction of the layer interfaces (defined as the y direction, with a maximum of nelemy elements in the y direction 61 of FIG. 19 ).
- the definition of a “sending” element is set forth below.
- a ‘numerical mesh’ 67 of FIG. 19 (which is the same ‘mesh’ as the ‘mesh’ which is shown in FIG. 8 that overlays the fracture footprint 46 ) consists of a mesh of rectangular shaped ‘elements’ or ‘grid cells’, such as ‘elements’ 67 a and 67 b , each rectangularly shaped ‘element’ or ‘grid cell’ 67 a , 67 b of FIG. 19 having a local dimension of ‘2a by 2b’ in the x and y directions 63 and 61 of FIG. 19 , respectively (the x direction 63 of FIG. 19 is defined to be parallel to the layer interface direction, in the plane of FIG. 4 ).
- a “sending” element will be defined in the following manner: Any element in the numerical mesh 67 can send stress data to any other element in the numerical mesh 67 . This is the way in which the influence coefficient matrix [C] 37 is populated—an element sending ‘stress data’ to another element is referred to as a “sending” element, and an element which receives and records such ‘stress data’ in the matrix [C] 37 is the “receiving” element.
- each element in the numerical mesh 67 takes its turn in being the “sending” element, and it sends stress data to all other elements, including itself, in the numerical mesh 67 , and all other elements are then “receiving” elements at which stress data is recorded. This process is repeated until all elements have in turn become “sending” elements and the matrix [C] 37 is fully populated.
- step 53 includes steps 53 a , 53 b , 53 c , 53 d , and 53 e .
- step 53 a we solve equation (8), which is set forth below as follows:
- ⁇ ⁇ zz l ⁇ ( m , n , y ) ⁇ p ⁇ A p l ⁇ ( k ) ⁇ c p l ⁇ ( m , n , y ) ⁇ e ⁇ p ⁇ ky ,
- UAS Uniform Asymptotic Solution
- step 53 c we invert the ‘Uniform Asymptotic Solution (UAS)’ analytically, as follows:
- step 53 d we invert the low frequency FT components ( ⁇ circumflex over ( ⁇ ) ⁇ zz l ) LOW numerically, as follows:
- FIGS. 17 and 18 Also not shown in FIGS. 17 and 18 is that we then increment the sending element number “iys” by 1 and repeat steps 49 , 51 , and 53 of FIGS. 17 and 18 for the next sending element. That is, after the steps 53 shown in FIG. 18 and the steps of storing and incrementing described immediately above, we return to step 49 of FIG. 17 .
- the ‘slip’ or debonding’ 27 between adjacent Earth formation layers 17 e and 17 f and between adjacent Earth formation layers 17 g and 17 h of FIGS. 4 and 5 may occur, and, as a result, fluid can propagate within the slip zone 27 , such as at the interface 31 between layers 17 e and 17 f of FIG. 5 .
- the slip zone 27 can stop the growth of the fracture 29 , and control the height of the fracture 29 . Therefore, it is important that the Hydraulic Fracturing Simulator software 80 of FIG. 10 model the ‘slip’ 27 or ‘debonding’ 27 of FIGS. 4 and 5 and its effect on the fracture 29 .
- the ‘slip’ 27 of FIGS. 4 and 5 can be modeled using the workstation or other computer system 72 shown in FIG. 10 .
- the input data 82 which is provided as input data to the computer system 72 of FIG. 10 , may include: reservoir layer rock properties, elastic constants per layer, confining stress in each layer, leakoff into the formation per layer, thickness of each layer, spring constants per layer interface, and fluid schedule.
- the input data 82 which is provided as input data to the computer system 72 of FIG. 10 would also include: the elastic Young's modulus E l and Poisson's ratio v l for each layer 17 a - 17 j of the formation 17 of FIG.
- the processor 72 a of FIG. 10 will execute the ‘Hydraulic Fracturing Simulator software’ 80 , which is embodied within the Planar 3D software 78 and the Planar 3D user interface 76 , while simultaneously using the ‘input data’ 82 as described above.
- the ‘output data’ 72 c 1 is generated, the ‘output data’ 72 c 1 being either printed as a printout on the recorder or display device 72 c or displayed on the display screen of recorder or display device 72 c of FIG. 10 .
- the ‘output data’ 72 c 1 may include the fracture footprint at each time step, the fluid pressure (p) and the fracture width (w) at each rectangularly shaped ‘element’ or ‘grid cell’ 48 a 1 of FIG. 8 and 67 a , 67 b of FIG. 19 associated with the ‘fracture footprint’ at times t 1 , t 2 , t 3 , . . . , t n shown in FIG. 4 , the distribution of proppant concentration, and other outputs of the simulator, such as fracture conductivity and net pressure.
- the ‘Hydraulic Fracturing Simulator software’ 80 (embodied within the Planar 3D software 78 and the Planar 3D user interface 76 ) is executed by the processor 72 a of the computer system 72 of FIG. 10 while using the input data 82 to generate the output data 72 c 1 , the following steps are practiced by the processor 72 a.
- the processor 72 a responsive to the input data 82 , executes the ‘Set Up Influence Coefficient Matrix [C]’ step 102 in FIG. 13 (and the ‘Generate Elastic Influence Coefficient Matrix for Parent Mesh’ step 102 in FIG. 15 which is the same step as step 102 in FIG. 13 ).
- the ‘Set Up Influence Coefficient Matrix [C]’ step 102 the ‘Influence Coefficient Matrix [C]’ 37 of the Elasticity Equation 33 of FIG.
- the Hydraulic Fracturing Simulator Software 80 to model and take into account the effect of the ‘slip’ 27 and/or the ‘debonding’ 27 between adjacent layers of a reservoir (such as between adjacent layers 17 e / 17 f and 17 g / 17 h ).
- the ‘Influence Coefficient Matrix [C]’ 37 is calculated in a ‘special way’ by the processor 72 a of computer system 72 , the processor 72 a executing the steps 47 , 49 , 51 and 53 of FIGS. 17 and 18 for the purpose of calculating the ‘Influence Coefficient Matrix [C]’ 37 of FIG. 14 in that ‘special way’.
- the processor 72 a begins the calculation of the ‘Influence Coefficient Matrix [C]’ 37 in that ‘special way’ by looping through each ‘sending element’ of the numerical mesh 67 of FIG. 19 in a direction that is orthogonal to the layer interfaces, defined as the y-direction 61 in FIG. 19 .
- the processor 72 a begins with ‘element or grid cell ( 67 a / 67 b of FIG. 19 ) number 1’ and ends with a maximum of ‘nelemy’ elements in the y-direction 61 .
- each ‘element or grid cell’ ( 67 a / 67 b ) in the numerical mesh 67 of FIG. 19 takes its turn in being the “sending” element, and it sends stress data to all other elements, including itself, in the numerical mesh 67 , and all other elements are then “receiving” elements at which stress data is recorded. This process is repeated until all ‘elements or grid cells’ ( 67 a / 67 b ) have, in turn, become “sending” elements, at which time, the ‘Influence Coefficient Matrix [C]’ 37 is fully populated.
- step 49 in FIG. 17 considering a rectangular ‘sending element’ [i.e., a ‘grid cell’ ( 67 a / 67 b ) of FIG. 19 ] having dimensions ( 2 a ) ⁇ ( 2 b ) located at [x(1), y(iys)] in layer l (step 51 of FIG. 17 ), the processor 72 a now begins to execute step 53 of FIG. 18 .
- a rectangular ‘sending element’ i.e., a ‘grid cell’ ( 67 a / 67 b ) of FIG. 19 ] having dimensions ( 2 a ) ⁇ ( 2 b ) located at [x(1), y(iys)] in layer l (step 51 of FIG. 17 )
- the processor 72 a now begins to execute step 53 of FIG. 18 .
- step 53 a in connection with the ‘current sending element’ or the ‘current grid cell 67 a / 67 b of FIG. 19 ’, solve equation (8) for the ‘current sending element’ to thereby yield a Fourier Transform (FT) of the ‘benchmark stresses’, which we represent by the notation ⁇ circumflex over ( ⁇ ) ⁇ zz l , where equation (8) is set forth in greater detail in the ‘Detailed Description’ of this specification, and is duplicated below, as follows:
- FT Fourier Transform
- step 53 b and 53 b 1 determine the ‘low frequency components (LOW)’ by subtracting off the 3-layer and 2-interface ‘Un
- T l ⁇ ( x , y , z ) 1 ( 2 ⁇ ⁇ ⁇ ) 2 ⁇ ⁇ - ⁇ ⁇ ⁇ ⁇ - ⁇ ⁇ ⁇ e - i ⁇ ( mx + nz ) ⁇ T ⁇ l ⁇ ( m , n , y ) ⁇ d m ⁇ d n ( 5 ) (4)
- FT low frequency Fourier Transform
- T l ⁇ ( x , y , z ) 1 ( 2 ⁇ ⁇ ⁇ ) 2 ⁇ ⁇ - ⁇ ⁇ ⁇ ⁇ - ⁇ ⁇ ⁇ e - i ⁇ ( mx + nz ) ⁇ T ⁇ l ⁇ ( m , n , y ) ⁇ d m ⁇ d n ( 5 ) (5)
- ⁇ zz l ( ⁇ zz l Low +( ⁇ zz l ) UAS
- Increment the old ‘sending element’ number i.e., the old ‘rectangularly shaped element or old grid cell’ 67 a / 67 b of FIG. 19
- the incrementing step is practiced by adding 1 to the old ‘sending element’ number iys, and repeat steps 49 , 51 , and 53 of FIGS. 17 and 18 for the next sending element.
- the processor 72 a After completion of steps 49 , 51 , and 53 for all sending elements (i.e., all the ‘rectangularly shaped elements or grid cells’ 67 a / 67 b ) in the numerical mesh 67 of FIG. 19 , the processor 72 a will store the ‘Influence Coefficient Matrix [C]’ 37 on a storage device for later use by step 92 of the Hydraulic Fracturing Simulator software 80 of FIG. 13 .
- step 53 of FIG. 18 When execution of step 53 of FIG. 18 is complete, a ‘new Influence Coefficient Matrix [C]’ 37 will be generated, where the ‘new Influence Coefficient Matrix [C]’ 37 will now allow the Hydraulic Fracturing Simulator software 80 to model and take into account the existence of ‘slip’ 27 or ‘debonding’ 27 between adjacent layers of the reservoir of FIG. 4 , such as the ‘slip’ 27 or ‘debonding’ 27 which exists between adjacent layers 17 e / 17 f and adjacent layers 17 g / 17 h of the reservoir or Earth formation 17 illustrated in FIG. 4 .
- step 102 illustrated in FIGS. 13 and 15 is now complete; and, as a result, the processor 72 a will now begin to execute the remaining steps of ‘Hydraulic Fracturing Simulator Software’ 80 illustrated in FIGS. 13 and 15 including steps 92 , 94 , and 96 .
- the ‘calculate fracture width (w), given fluid pressure (p) (multilayer elasticity)’ step 92 of FIG. 13 will be executed by the processor 72 a of the computer system 72 of FIG. 10 .
- the ‘new Influence Coefficient Matrix [C]’ 37 which was calculated using FIGS. 17 and 18 as described above, will be used in connection with the Influence Coefficient Matrix [C] 37 of the Elasticity Equation 33.
- the term ⁇ c is the local confining stress which can vary from one layer to the next.
- An initial, estimated, value of the fluid pressure (p) will be selected. Therefore, using the ‘new Influence Coefficient Matrix [C]’ which was calculated using FIGS. 17 and 18 as described above, and using the values of p and ⁇ c previously described, the fracture width (w) will be calculated in second step 92 of FIG. 13 by the processor 72 a of the computer system 72 of FIG. 10 .
- the ‘calculate fluid pressure (p) given fracture width (w) (fluid flow)’ step 94 of FIG. 13 will now be executed by the processor 72 a .
- the fluid pressure (p) will be calculated using the fracture width (w) that was calculated in the second step 92 of FIG. 13 , as described above.
- the second step 92 and the third step 94 will iterate on each other (as indicated by arrow 100 ) until the fracture width (w) and the fluid pressure (p) are solved at every point in the fracture geometry of FIG. 4 .
- the fracture footprint is updated in step 96 of FIG. 13 .
- the time step 97 is then incremented to the second time step t 2 , and, responsive thereto, the second step 92 and the third step 94 will then iterate again on each other (as indicated by arrow 100 ) until the fracture width (w) and the fluid pressure (p) are solved at every point in the fracture geometry of FIG. 4 .
- the fracture footprint is updated in step 96 .
- the time step 97 is then incremented once again to the third time step t 3 , and the second step 92 and the third step 94 will then iterate again on each other (as indicated by arrow 100 ) until the fracture width (w) and the fluid pressure (p) are solved at every point in the fracture geometry of FIG. 4 .
- the fracture footprint is updated again in step 96 , the time step 97 is then incremented once again, and the above process repeats until ‘convergence’ is achieved.
- the aforesaid ‘convergence’ will be achieved when the difference between the fracture width (w) of step 92 in the current iteration of loop 100 and the fracture width (w) of step 92 in the previous iteration of loop 100 is less than or equal to a small value ⁇ , and the difference between the fluid pressure (p) of step 94 in the current iteration of loop 100 and the fluid pressure (p) of step 94 in the previous iteration of loop 100 is less than or equal to a small value ⁇ .
- the Output Data 72 c 1 of FIG. 13 is generated when the aforementioned ‘convergence’ is achieved.
- the Output Data 72 c 1 may include: the fracture footprint at each time step, fluid pressure (p), and fracture width (w) at each ‘element’ or ‘grid cell’ of the fracture footprint.
- u 1,3 for example, is defined as
- T l ( ⁇ yy l , ⁇ yx l , ⁇ yz l ,u y l ,u x l ,u z l )
- K l is a differential operator
- superscript T denotes the mathematical transpose operator
- b l is a body forcing term that is zero in our case.
- g ⁇ ⁇ ( m , n ) ⁇ - ⁇ ⁇ ⁇ ⁇ - ⁇ ⁇ ⁇ e i ⁇ ( mx + nz ) ⁇ ⁇ g ⁇ ( x , z ) ⁇ d x ⁇ ⁇ d z
- Z l (k, y) is a 6 by 6 matrix that depends on the elastic constants of the layer in which the solution is desired, the wave-number k, and y, which determines the horizon in a particular layer at which the solution is required, and is defined by equation (3.5) in the following reference: A. P. Peirce, and E. Siebrits, “Uniform Asymptotic Approximations for Accurate Modeling of Cracks in Layered Elastic Media”, International Journal of Fracture, 110, 205-239, 2001.
- a l (k,y) is a 6 by 1 column vector of integration constants parameterized by k.
- R terms are defined by (3.14) to (3.18) in the following reference: A. P. Peirce, and E. Siebrits, “Uniform Asymptotic Approximations for Accurate Modeling of Cracks in Layered Elastic Media”, International Journal of Fracture, 110, 205-239, 2001, the disclosure of which is incorporated by reference into this application.
- the undetermined coefficients A l (k) for each layer can be calculated using equation (3).
- T l ⁇ ( x , y , z ) 1 ( 2 ⁇ ⁇ ) 2 ⁇ ⁇ - ⁇ ⁇ ⁇ ⁇ - ⁇ ⁇ ⁇ e - i ⁇ ( mx + nz ) ⁇ T ⁇ l ⁇ ( m , n , y ) ⁇ d m ⁇ d n ( 5 ) 4. Slip Interface Conditions
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Abstract
Description
{w}=[C]−1{p−σc}, where Elasticity Equation 33:
- ‘w’ is the
fracture width 35, - ‘[C]’ is the ‘matrix of influence coefficients’ 37, and superscript ‘−1’ indicates its inverse,
- ‘p’ is the
fluid pressure 39, and - ‘σc’ is the confining
stress 41.
Δu l =u b l+1 u t l =R bt l+1 p t l+1+(R bb l+1 −R tt l)p t l −R tb l p t l+1 +R bb l+1 Δp l −R tb l Δp l−1 (4)
{circumflex over (T)} l(k, y)=Z l(k, y)A l(k) (3)
({circumflex over (σ)}zz l)LOW={circumflex over (σ)}zz l−({circumflex over (σ)}zz l)UAS
σzz l=(σzz l)LOW+(σzz l)UAS (equation 53e1)
(2) In
({circumflex over (σ)}zz l)LOW={circumflex over (σ)}zz l−({circumflex over (σ)}zz l)UAS,
(3) In
(4) In
(5) In
σzz l=(σzz l Low+(σzz l)UAS
‘C(numr,iys)=σzz l(ixr,iyr), where numr=(ixr−1)*nelemy+iyr’].
{w}=[C]−1{p−σc} (Elasticity Equation 33)
Equilibrium: σij,j l +f i l−0 (1a)
σij,j=σ11,1+σ12,2+σ13,3, σ2j,j=σ21,1+σ22,2+σ23,3, and σ3j,j=σ31,1+σ32,2+σ33,3,
and σ12,2, for example, is defined as
where x1≡x, x2≡y, and x3≡z.
Stress-strain: σij l=λlεkk lδij+2 μlεij l (1b)
Strain-displacement: εij l=(u i,j l +u j,i l)/2 (1c)
∂y T l =K l T l +b l (2a)
∂y {circumflex over (T)} l ={circumflex over (K)} l(k){circumflex over (T)}l +{circumflex over (b)} l (2b)
{circumflex over (T)} l(k, y)=Z l(k, y)A l(k) (3)
{circumflex over (T)} l=(p l ,u l)T (3a)
Δu l =u b l+1 −u t l =R bt l+1 p t l+1+(R bb l+1 −R tt l)p t l −R tb l p t l+1 +R bb l+1 Δp l −R tb l Δp l−1 (4)
4. Slip Interface Conditions
σyx l =k yx(u x l+1 −u x l)|y→y
σyz l =k yz(u z l+1 −u z l)|y→y
Δσyy l=0
Δσyx l=0
Δσyz l=0
σyx l=kyxΔux l
σyz l=kyzΔuy l
Δuy l=0 (7)
-
- (1) “Some Applications of the Frictionless Laminated Model”, Rock Mechanics as a Guide for Efficient Utilization of Natural Resources, Khair (ed.), copyright 1989, Balkema, Rotterdam,
ISBN 90 6191 871 5; - (2) “Subsidence Prediction Using a Laminated Linear Model”, Rock Mechanics as a Guide for Efficient Utilization of Natural Resources, Khair (ed.), copyright 1989, Balkema, Rotterdam,
ISBN 90 6191 871 5; and - (3) “Backward Transfer-Matrix Method for Elastic Analysis of Layered Solids with Imperfect Bonding”, Journal of Elasticity, 50: 109-128, 1998, copyright 1998 Kluwer Academic Publishers
- (1) “Some Applications of the Frictionless Laminated Model”, Rock Mechanics as a Guide for Efficient Utilization of Natural Resources, Khair (ed.), copyright 1989, Balkema, Rotterdam,
Claims (34)
({circumflex over (σ)}zz l)LOW={circumflex over (σ)}zz l−({circumflex over (σ)}zz l)UAS,
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Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20040254730A1 (en) | 2002-01-31 | 2004-12-16 | Najmuddin Ilyas Juzer | Method and apparatus for detecting fractures using frequency data derived from seismic data |
US6985816B2 (en) * | 2003-09-15 | 2006-01-10 | Pinnacle Technologies, Inc. | Methods and systems for determining the orientation of natural fractures |
Family Cites Families (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6131071A (en) * | 1996-12-06 | 2000-10-10 | Bp Amoco Corporation | Spectral decomposition for seismic interpretation |
US5870691A (en) * | 1996-12-06 | 1999-02-09 | Amoco Corporation | Spectral decomposition for seismic interpretation |
RU2119679C1 (en) * | 1997-12-05 | 1998-09-27 | Станислав Васильевич Васильев | Method for searching and prospecting of oil and gas deposits |
-
2005
- 2005-03-31 US US11/096,047 patent/US7386431B2/en not_active Expired - Fee Related
-
2006
- 2006-03-29 CA CA2541459A patent/CA2541459C/en not_active Expired - Fee Related
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Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20040254730A1 (en) | 2002-01-31 | 2004-12-16 | Najmuddin Ilyas Juzer | Method and apparatus for detecting fractures using frequency data derived from seismic data |
US6985816B2 (en) * | 2003-09-15 | 2006-01-10 | Pinnacle Technologies, Inc. | Methods and systems for determining the orientation of natural fractures |
Non-Patent Citations (42)
Title |
---|
A. A. Linkova and A. A. Savitski, An Effective Method for Multi-layered Media with Cracks and Cavities, p. 338-355, (1994) International Journal of Damage Mechanics, vol. 3. |
A. Peirce, E. Seibrits "Stability Analysis and Design of Time Stepping Schemes for General Elastodynamic Boundary Element Models", International Journal for Numerical Methods in Engineering, vol. 40, pp. 319-342 (1997). * |
Anthony P. P,eirce, Eduard Siebrits, "Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media" International Journal of Fracture, Jan. 31, 2001, pp. 205-239. * |
Ben-Menahem, A. and Singh, S.J. 1968. Multipolar Elastic Fields In A Layered Half Space, Bull. Seism. Soc. Am. 58(5). 1,519-72. |
Cade Office, Solution Revolution Break Open Your Reserves with FracCADE, p. 1-6, (Jan. 1998), Schlumberger Oilfield Services, Dowell, GeoQuest. |
Chen. W.T. 1971. Computation Of Stresses And Displacements In A Layered Elastic Medium. Int.J. Engng Sci. vol. 9. 775-800. |
Chow, Y.L., Yang, J.J. and Howard, G.E. 1991. Complex Images For Electrostatic Computation In Multilayered Media. IEEE Trans. On Microwave Theory and Techniques. vol. 39.No. 7. 1120-25. |
Crampagne, R. Ahmadpanah, M and Guiraud, J.L. 1978. A Simple Method For Determining The Green's Function For A Class Of MIC Lines Having Multilayered Dielectric Structures. IEEE Trans. On Microwave Theory and Techniques. vol. MTT-26.No. 2. 82-87. |
D. A. Mendelsohn, A Review of Hydraulic Fracture Modeling-Part I: General Concepts, 2D Models, Motivation for 3D Modeling, p. 369-376, (Sep. 1984), Journal of Energy Resources Technology. |
Dr. Quan Guo, A Fully Three-Dimensional Hydraulic Fracturing Simulator, p. 1-14, TerraFrac (Jan. 1, 1995). |
Dushan B. Jovanovic, Moujahed I. Husseini and Michael A. Chinnery, Elastic Dislocations in a Layered Half-Space-I. Basic Theory and Numerical Methods, p. 205-217, (1974), Geophys. J. R. astr. Soc. 39. |
Ernian Pan, Stastic Response of a Transversely Isotropic and Layered Half-Space to General Surface Loads, p. 353-363, Physics of the Earth and Planetary Interiors, 54, 1989. |
Ernian Pan, Static Green's Function in Multilayeres Halfspaces, p. 509-521, (1997), Appl. Math. Modeling, vol. 21. |
Ernian Pan, Static Response of a Transversely Isotropic and Layered Half-Space to General Dislocation Sources, p. 103-115, (1989), Physics of the Earth and Planetary Interiors, 58. |
FracCade Software, p. 1-4, Schlumberger Dowell, (Jan 1, 1995). |
Gohfer Grid Oriented Hydraulic Fracture Extension Replicator, p. 1-52, Appendix, p. 1-11, (1996) by Stim-Lab, Inc. and Marathon Oil Company. |
J. A. Ryder and J. A. L. Napier, Error Analysis and Design of a Large-Scale Tabular Mining Stress Analyser, (1985) Chamber of Mines of South Africa Research Organization. |
J.A. Ryder, Cairns, E.G. Beer, J.R. Booker, and J.P. Carter, Optimal Iteration Schemes Suitable For General Non-Linear Boundary Element Modeling Applications: Proceedings for the 7<SUP>th </SUP>International Conference on Computer Methods and Advances in Geomechanics, Balkema Rotterdam, 1991. |
J.A. Ryder, Optimal iteration schemes suitable for general non-linear boundary element modeling applications, pp. 1079-1084, (1991), Rock Engineering Division, COMRO, South Africa. |
Jovanovich, D.B. Husseini, M.I. and Chinnery, M.A. 1974. Elastic Dislocations In A Layered Half-Space-I. Basic Theory And Numerical Methods. Geophys. J.R., Astro. Soc. 39.205-217. |
L. J. Wardle, Stress Analysis of Multilayered Anisotropic Elastic Systems Subject to Rectangular Loads, p. 1-37, (1980) CSIRO. |
Linkov,A.M. Linkova, A.A. and Savitski, A.A. 1994. An Effective Method For Multi-layered Media With Cracks and Cavities. Int. J. of Damage Mech. 3. 338-35. |
P. Peirce, and E. Siebrits, "Uniform Asymptotic Approximations For Accurate Modeling of Cracks in Layered Elastic Media", International Journal of Fracture, 110, 205-239-, 2001. |
Pan E. 1989. Static Response Of A Transversely Isotropic And Layered Half-Space To General Dislocation Sources. Physics of the Earth and Planetary Interiors, 58. 103-117. |
Pan, E. 1989, Static Response Of A transversely Isotropic And Layered Half-Space To General Surface Loads. Physics of the Earth and Planetary Interiors. 54. 353-363. |
Pan, E. 1997. Static Green's Functions In Multilayered Half Spaces. Appl. Math. Modeling. 21, 509-521. |
Pichmony Anhaouy, "Numerical Solution of a Fluid Driven Fracture Problem" Institute of Applied Mathematics, The University of British Columbia, Vancouver, British Columbia, Canada, Apr. 22, 2003, pp. 1-60. * |
R.J. Clifton, Three-Dimensional Fracture-Propagation Models, p. 95-108, Brown U. and Terra Tek Inc. (Jan. 1, 1989). |
Raymond Crampagne, Majid Ahmadpanah, and Jean-Louis Guiraud, A Simple Method for Determining the Green's Function for a Large Class of MIC Lines Having Multilayered Dielectric Structures, p. 82-87 (1978) IEEE. |
Ryder, J.A. and Napier, J.A. L. 1985. Error Analysis and Design Of A Large Scale Tabular Mining Stress Analyzer. Proc: Fifith Int. Conf. On Num. Meth. In Geomech. Nagoya. 1549-1555. |
Ryosuke Sato and Mitsuhiro Matsu'ural, Static Deformations Due to the Fault Spreading over Several Layers in a Multi-Layered Medium Part I: Displacement, p. 227-249, (Sep. 20, 1973), J. Phys. Earth, 21. |
Salamon M., "Some Application of the Frictionless Laminated Model". Rock Mechanics as a Guide for Efficient Utilization of Natural Resources, Khair (ed.), copyright 1989, Balkema, Rotterdam, ISBN 90 6191 871 5. |
Salamon M., "Subsidence Prediction Using a Laminated Linear Model", Rock Mechanics as a Guide for Efficient Utilization of Natural Resources, Khair (ed.), copyright 1989, Balkema Rotterdam, ISBN 90 6191 8715. |
Sarva Jit Singh, Static Deformation of a Multilayered Half-Space by Internal Sourcesp. 3257-3263. (Jun. 10, 1970), Journal of Geophysical Research. |
Sarva Jit Singh, Static Deformation of a Transversely Isotropic Multilayerd Half-Space by Surface Loads, p. 263-273, (1986), Physics of the Earth and Planetary Interiors, 42. |
Sato, R. and Matsu'ura, M. 1973. Static Deformations Due To The Fault Spreading Over Several Layers In A Multi- Layered Medium Part I: Displacement. J.Phys. Earth. 21. |
Singh, S.J. 1970. Static Deformation Of A Multi-Layered Half-Space By Internal Sources. J. Geophys. Res. 75(17). 3,257-63. |
Singh, S.J. 1986. Static Deformations Of A Transversely Isotropic Multilayered Half-Space By Surface Loads. Physics of the Earth and Planetary Interiors. 42. 263-273. |
W. T. Chen, Computation of Stresses and Displacements in a Layered Elastic Medium, p. 775-800 (1971) Int. J. Engng Sci. vol. 9. |
Wardle, L.J. 1980. Stress Anaylsis Of Multilayered Anisotropic Elastic Systems Subject To Rectangular Loads, CSIRO Aust. Div. Appl. Geomech. Tech. paper No. 33. 1-37. |
Y. Leonard Chow, Jian Jun Yang, and Gregory E. Howard, Complex Images for Electrostatic Field Computation in Multilayered Media, P. 1120-1125, (1991) IEEE. |
Yue, Z. and Yin J., "Backward Transfer-Matrix Method for Elastic Analysis of Layered Solids with Imperfect Bonding", Journal of Elasticity, 50: 109-128, 1998 copyright 1998 Kluwer Academic Publishers. |
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